Football physics & perception

SEED has a nice story on perception of curving shots in football (soccer).

The physics of the curving trajectory is interesting. In short, a light spinning ball can transition from a circular trajectory to a tighter spiral, surprising the goalkeeper.

What I find really interesting, though, is that goalkeepers don’t anticipate this.

But goalkeepers see hundreds of free kicks in practice on a daily basis. Surely they’d eventually adapt to bending shots, wouldn’t they?

… Elite professionals from some of the top soccer clubs in the world were shown simulations of straight and bending free kicks, which disappeared from view 10 to 12.5 meters from the goal. They then had to predict the path of the ball. The players were accurate for straight kicks, but they made systematic errors on bending shots. Instead of taking the curve into account, players tended to assume the ball would continue straight along the path it was following when it disappeared. Even more surprisingly, goalkeepers were no better at predicting the path of bending balls than other players. …

I think the interesting question is, could they be trained to anticipate this? It’s fairly easy for the goalie to observe the early trajectory of a ball, but due to the nonlinear transition to a new curvature, that’s not helpful. To guess whether the ball might suddenly take a wicked turn, one would have to judge its spin, which has to be much harder. My guess is that prediction is difficult, so the only option is to take robust action. In the case of the famous Carlos shot, one might guess that the goalie should have moved to cover the pole, even if he judged that the ball would be wide. (But who am I to say? I’m a lousy soccer player – I find 9 year olds to be stiff competition.)

SEED has another example:

I wrote about a similar problem on my blog earlier this year: How baseball fielders track fly balls. Researchers found that even when the ball is not spinning, outfielders don’t follow the optimum path to the ball—instead they constantly update their position in response to the ball’s motion.

At first this sounds like a classic lion-gazelle pursuit problem. But there’s one key difference: in pursuit problems I’ve seen, the opponent’s location is known, so the questions are all about physics and (maybe) strategic behavior. In soccer and baseball, at least part of the ball’s state (spin, for example) is at best poorly observed by the receiver. Therefore trajectories that appear to be suboptimal might actually be robust responses to imperfect measurement.

The problems faced by goalies and outfielders are in some ways much like those facing managers: what do you do, given imperfect information about a surprisingly nonlinear world?

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